Theorem orim2d 795

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)

Hypothesis

Ref	Expression
orim1d.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
orim2d	|- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Proof of Theorem orim2d

Step	Hyp	Ref	Expression
1		idd 21	. 2 |- ( ph -> ( th -> th ) )
2		orim1d.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	orim12d 793	1 |- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Syntax hints:   -> wi 4   \/ wo 715

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 716

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  796  orbi2d  797  pm2.82  819  stdcndcOLD  853  pm2.13dc  892  exmid1dc  4290  acexmidlemcase  6012  poxp  6396  fodjuomnilemdc  7342  omniwomnimkv  7365  exmidontriimlem1  7435  indpi  7561  suplocexprlemloc  7940  nneoor  9581  uzp1  9789  maxabslemlub  11767  xrmaxiflemlub  11808  nninfctlemfo  12610  exmidunben  13046  bj-nn0suc  16559  sbthomlem  16629